<div class="problem-statement">
 <div class="header">
  <div class="title">
   G. Cycle Palindrome
  </div>
  <div class="time-limit">
   <div class="property-title">
    time limit per test
   </div>1 second
  </div>
  <div class="memory-limit">
   <div class="property-title">
    memory limit per test
   </div>256 megabytes
  </div>
  <div class="input-file">
   <div class="property-title">
    input
   </div>standard input
  </div>
  <div class="output-file">
   <div class="property-title">
    output
   </div>standard output
  </div>
 </div>
 <div>
  <p>We say that a sequence of $n$ integers $a_1, a_2, \ldots, a_n$ is a palindrome if for all $1 \leq i \leq n$, $a_i = a_{n-i+1}$. You are given a sequence of $n$ integers $a_1, a_2, \ldots, a_n$ and you have to find, if it exists, a <span class="tex-font-style-it">cycle permutation</span> $\sigma$ so that the sequence $a_{\sigma(1)}, a_{\sigma(2)}, \ldots, a_{\sigma(n)}$ is a palindrome. </p>
  <p>A permutation of $1, 2, \ldots, n$ is a bijective function from $\{1, 2, \ldots, n\}$ to $\{1, 2, \ldots, n\}$. We say that a permutation $\sigma$ is a cycle permutation if $1, \sigma(1), \sigma^2(1), \ldots, \sigma^{n-1}(1)$ are pairwise different numbers. Here $\sigma^m(1)$ denotes $\underbrace{\sigma(\sigma(\ldots \sigma}_{m \text{ times}}(1) \ldots))$.</p>
 </div>
 <div class="input-specification">
  <div class="section-title">
   Input
  </div>
  <p>The input consists of multiple test cases. The first line contains a single integer $t$ ($1 \leq t \leq 3 \cdot 10^4$) — the number of test cases. Description of the test cases follows.</p>
  <p>The first line of each test case contains an integer $n$ ($2 \leq n \leq 2 \cdot 10^5$) — the size of the sequence.</p>
  <p>The second line of each test case contains $n$ integers $a_1, \ldots, a_n$ ($1 \leq a_i \leq n$).</p>
  <p>The sum of $n$ for all test cases is at most $2 \cdot 10^5$.</p>
 </div>
 <div class="output-specification">
  <div class="section-title">
   Output
  </div>
  <p>For each test case, output one line with <span class="tex-font-style-tt">YES</span> if a cycle permutation exists, otherwise output one line with <span class="tex-font-style-tt">NO</span>.</p>
  <p>If the answer is <span class="tex-font-style-tt">YES</span>, output one additional line with $n$ integers $\sigma(1), \sigma(2), \ldots, \sigma(n)$, the permutation. If there is more than one permutation, you may print any.</p>
 </div>
 <div class="sample-tests">
  <div class="section-title">
   Example
  </div>
  <div class="sample-test">
   <div class="input">
    <div class="title">
     Input
    </div>
    <pre>3
4
1 2 2 1
3
1 2 1
7
1 3 3 3 1 2 2
</pre>
   </div>
   <div class="output">
    <div class="title">
     Output
    </div>
    <pre>YES
3 1 4 2 
NO
YES
5 3 7 2 6 4 1 
</pre>
   </div>
  </div>
 </div>
</div>